Steve Clarke's side cantered to victory in Hungary thanks to two first-half goals from the French forward, while Graham Dorrans extended the lead late on from the penalty spot
The Frenchman scored his first goals for the club in the opening 30 minutes in Sopron, Hungary, before a late Graham Dorrans penalty wrapped up a comfortable win for Steve Clarke's team.
Shane Long returned for the Premier League outfit after he missed Thursday's 2-1 defeat to Hannover with a toe injury. The Ireland international started up-front alongside Anelka and Markus Rosenborg.
Chris Brunt had the first opportunity of the game when he forced Ludos Hayduch into a finger-tip save from a free kick. The visitors' captain then took the resulting corner, which Anelka duly poked home for the opening goal.
Long nearly doubled the lead in the 19th minute. He latched onto a Markus Rosenberg through ball, but his neat chip over the keeper came back off the post.
However, West Brom did not have to late long for a second. A fantastic one-two between Anelka and Rosenberg led to the Frenchman heading into the top-left hand corner.
The away side took their foot off the pedal slightly in the second period, as Uros Wilkolics and Polonkyi Attily both went close for the home side.
But with the game heading into the last ten minutes, Dorrans sewed up West Brom's win with an emphatic spot-kick after Kemar Roofe was felled in the box.